Problem: Solve for $x$ : $ 8|x + 1| + 7 = 2|x + 1| + 6 $
Explanation: Subtract $ {2|x + 1|} $ from both sides: $ \begin{eqnarray} 8|x + 1| + 7 &=& 2|x + 1| + 6 \\ \\ { - 2|x + 1|} && { - 2|x + 1|} \\ \\ 6|x + 1| + 7 &=& 6 \end{eqnarray} $ Subtract ${7}$ from both sides: $ \begin{eqnarray} 6|x + 1| + 7 &=& 6 \\ \\ { - 7} &=& { - 7} \\ \\ 6|x + 1| &=& -1 \end{eqnarray} $ Divide both sides by ${6}$ $ \dfrac{6|x + 1|} {{6}} = \dfrac{-1} {{6}} $ Simplify: $ |x + 1| = -\dfrac{1}{6}$ The absolute value cannot be negative. Therefore, there is no solution.